1 . 定义:
表示不大于
的最大整数,
表示不小于
的最小整数,如
,
.设函数
在定义域
上的值域为
,记
中元素的个数为
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af9bbe98100c8067ff36ac536d043a85.png)
________ ,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab342d472fe409e73bee1be8a61774d3.png)
_______
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25f161c2a3717f1b6c62d0d7dae0b606.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f3788a125c33eee076151e215a9b02b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd5b5087fa6a0f43820031bdbbf38b26.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d51d711c88c076b32b158d10f35b209b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ad3f020a093c17c56ebe159f34b962c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1400a767b094cae877a340dc2467edc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcc31dcdb99754fc452ff2b92a2fb8c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcc31dcdb99754fc452ff2b92a2fb8c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af9bbe98100c8067ff36ac536d043a85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab342d472fe409e73bee1be8a61774d3.png)
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2 . 将函数
的零点按照从小到大的顺序排列,得到数列
,其前
项和为
,且
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9448bf1d6136b3a108e7ea60506ad39.png)
______ ,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04c2864e2ec3416cc4c081ac1f71a0af.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9c3cc4ba626cc12074542728cdfb930.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/352d9b76dcf639368fa68cae70149802.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9448bf1d6136b3a108e7ea60506ad39.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04c2864e2ec3416cc4c081ac1f71a0af.png)
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3 . 在正项无穷数列
中,若对任意的
,都存在
,使得
,则称
为
阶等比数列.若
为1阶等比数列,且
,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3f7fda69e2b32b9ced2239f915fa59b.png)
_________ ;若数列
是2阶等比数列,且
,
,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6016be828be0c8e87f425f3b9437ba1.png)
_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/209559aca6bf32705588b6a40e0b7320.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49f62d620374c35e1d8d90b6f8b6e801.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a327da06d8bf19a6f0ce10089cf303d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a9e8b2a0eed594720eb8a65fefd714a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0223546f654f83bb6ebf4bb52e86157.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3f7fda69e2b32b9ced2239f915fa59b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59dd6c97d2ee3e74ba5730f1cbcc1d43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1bfdf0c734162745dcebe626bc59cc0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd4cf909f2febeea7d169459d0cf0bcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6016be828be0c8e87f425f3b9437ba1.png)
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4 . 若正整数集
的非空子集
满足:至少含有2个元素,且任意两个元素之差的绝对值大于1,则称
为数集
的超子集.对于集合
,记
的超子集的个数为
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26974cd38196094faf713e10668d42a2.png)
______ ,
与
的关系为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12934b832f1484fb88b13974e50cad4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12934b832f1484fb88b13974e50cad4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10937bdfe1d64b5f53b598b377f94312.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3cfeacc29e6a61c5b3b4e439c0a91df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26974cd38196094faf713e10668d42a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a69725055853cf456a3c92632bd54dbe.png)
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5 . 将正奇数按如图所示的规律排列:
在第________ 行,从左向右第________ 个数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e946baf1316ac1f219398ecedadf6cf.png)
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6 . 某牧场今年初牛的存栏数为1200,预计以后每年存栏数的增长率约为10%,且每年年底卖出100头牛.设牧场从今年起的十年内每年年初的计划存栏数依次为
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdec83c1d97d4547ac547d628a00c57f.png)
_______ ,数列
的通项公式
_______ ( 1≤n≤10,
).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3da1bb29672197592e16df4da68c69d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdec83c1d97d4547ac547d628a00c57f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3783e69ef5a6a0af566ff4e21ccf03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/610e5598d7ded93073255ec6ffffa677.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e962057e0daa783fc1161ce3bb3c30d9.png)
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49次组卷
|
2卷引用:江苏省华罗庚中学2024届高三下学期5月适应性考试数学试卷
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7 . 命题:若
是等比数列,则前n项和
不存在最大值和最小值.写出一组说明此命题为假命题的首项![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7999465d0e871febde66296a0cbf058c.png)
___________ 和公比![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad0d99fef1aa4dbcc6dc7b30b7d2c9a9.png)
___________
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7999465d0e871febde66296a0cbf058c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad0d99fef1aa4dbcc6dc7b30b7d2c9a9.png)
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8 . 已知数列
的首项
,且
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25960d3812de00a90f060950f4b48197.png)
______ ;满足
的最大整数
的值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc6545b8eca1c4223ed701a199a85683.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7643e8b7aa32ebf299048417a94432dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25960d3812de00a90f060950f4b48197.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b9587d657211fcc4d689e81ea186c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
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9 . 汉代刘歆设计的“铜嘉量”是龠、合、升、斗、斛五量合一的标准量器,其中升量器、斗量器、斛量器的形状均可视为圆柱.若升、斗、斛量器的容积成公比为10的等比数列,底面直径依次为
,且斛量器的高为
,则斗量器的高为______
,升量器的高为________
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d40bfea5eaefd08ce28476a2708262b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac5f863463679148ff8f85329744fd05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21f3bf70722b22983c120d008d097602.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21f3bf70722b22983c120d008d097602.png)
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2285次组卷
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6卷引用:2024年北京高考数学真题
2024年北京高考数学真题专题07立体几何与空间向量(已下线)2024年北京高考数学真题变式题11-15专题08立体几何与空间向量(第一部分)(已下线)五年北京专题06立体几何与空间向量(已下线)三年北京专题06立体几何与空间向量
10 . 一质点在平面内每次只能向左或向右跳动1个单位,且第1次向左跳动.若前一次向左跳动,则后一次向左跳动的概率为
;若前一次向右跳动,则后一次向左跳动的概率为
.记第n次向左跳动的概率为
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e948956b4ef1bb5fa3c09fbda213dee.png)
________ ;![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f11c04103c0e5416897894d9225637b2.png)
________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dac452fbb5ef6dd653e7fbbef639484.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ffb021aa7d5a5c2f0691e337caad624.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e948956b4ef1bb5fa3c09fbda213dee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f11c04103c0e5416897894d9225637b2.png)
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